Add the dried chiles, halved white onion, and tomatoes in a Dutch oven or large lidded pot (if using Mexican cinnamon, add it now). Fill to cover with cold water and bring to a simmer over medium heat. Cover, reduce heat, and continue to simmer for 15 minutes.
Strain peppers/onion/tomatoes from the liquid and add to a blender with all spices, cinnamon, salt, pepper, garlic, broth, and vinegar. Blend for 2 minutes or until smooth. You can optionally fine strain afterwards to remove any solids. Add more salt to taste as needed.
Season chicken liberally with salt. Heat a generous splash of oil in the same Dutch oven over medium heat. Sear the chicken for 2-3 minutes per side. Pour the sauce (consomé) over the chicken. Bring to a simmer and cook for 10-15 minutes or until chicken reaches an internal temp of 165°F.
Remove chicken and add to a bowl. Finely shred and top with extra sauce to taste. Heat oil in a cast iron skillet or pan. Dip the tortillas in the top of the consomé (ideally soaking up the fatty top layer) and sear in the skillet/pan. Top half with cheese, shredded chicken, more cheese, fold over, and flip. Sear until crisp and store in oven at low heat as you prepare the rest.
Serve with a side of consomé topped with chopped onion and cilantro for dipping.